Professor Fox opened the door to the familiar Arithmancy classroom and stepped inside, standing behind the main desk. He then turned around and wrote on the board:

Professor Fox then distributed small, personal chalk boards to all the students and returned to the front of the classroom, waiting patiently for class to start.

[OOC Note: My computer is not behaving itself lately and long story short, the content of this lesson plan may not be as organized as usual, please bear with me. Also, if I should disappear for an hour or so on end behave yourselves as other mods will be checking the thread should I mysteriously vanish. Good luck to us all.]

Nadia walked into the classroom and took a seat. She decided a desk near the blackboard would be better especially with this subject. As she waited for class to start, she took a couple of things from her bag, including a book and notes and kept working on... well, do I need telling?

Terry walks into class to discover she is the first student here. She finds a seat and gets out her Arithmancy book, parchment, ink, and quill. She then opens her book to composite numbers. Terry read the chapter last night in anticipation of this class, but she could not make heads nor tails out of the material. She hoping the professor's lecture will clear somethings up.

Lily walks into the classroom and sees only 2 other students. She sits down next to Terry and writes on her personal chalkboard:

She arranges her things around her and leans back in her chair. "Hi," she whispers to Terry, unsure if she can talk or not. "I'm Lily. You're Terry, right?"

Terry looks up from her book. "Yes my names Terry. Nice to meet you Lily."

Lee hadn't attended an Arthimancy lesson at all this year due to the loss of his old one, Professor Bree. However he had plucked up the courage to attend todays lesson and took a seat in the back. Besides he needed to get a bigger idea of this Fox character.

Lee got his equipment out and placed it on his desk. Reading the board he did as it instructed. Taking his chalkboard he wrote in his loopy Hufflepuffish writing:

Quote:

Lee Andrez
Hufflepuff
3rd Year

Once this was done he placed it back onto his desk and waited for something to do. He needed to talk to Erica about some matters and Terry also. He thought it best to leave it after class, especially while Fox was present.

Picking the conversation by two fellow school mates, Nadia looks up and now realizes she had forgotten to write her name and house as the professor had asked them at the board. She had done that before and forgot now. So, just to be redundant, she wrote the name (Nadia Chantalona Rey, though she was not expecting Fox to use her full name) and house and year. She was idly reminded of kindergarden...

Alex enetered the Arithmancy classroom and gave Professor a polite nod. "Professor," she muttered before making her way to her usual seat, at the back of the classroom.

She scribbled down her full name (Alexandra Diana Kay), her house (Slytheirn) and her year (Fourth). Afterwards, the Slytherin girl pushed the chalkboard off on the side of the desk and rested her gaze on the Professor while awaiting quietly for class to begin.

Professor Fox sighed to himself. It seemed the more time that passed the fewer students came to his lectures. He turned his attention to the students in his classroom, "Well students, we will begin in a little bit, I would ike to wait a bit longer to see how many more students arrive. Then we will begin and any students not here will simply have to wander in."

Erica strolled into the classroom and took a seat, relieved that she was not late for the class. Following the usual procedures for Fox, she wrote her name, year and house on the small chalkboard the professor provided and patiently waited for the class to begin.

Xavier hurries into the classroom, hoping he wasn't late. As he enters through the doorway he realized he was just in time. He sits down at the first desk he finds.

Reaching into his bag he removes his Arithmancy books, although he thought it unlikely he would use them.

Professor Fox checked the time and sighed. He picked up a piece of chalk and wrote neatly on the board:

Review of Identity Numbers:

"Now, who can tell me two important aspects concerning our last lesson?" He asked the class.

Nadia raised her hand, "Identity numbers 1 and 0 are such because in certain operations, no matter which number they are paired with, they give the same number they were paired with.

"An aspect concerning zero is that it is used to mean decadence and how all things can be reduced to zero, that is, nothingness. One (1) represents unity."

Professor Fox nodded. "Excellent answer Ms. Rey. Though, I would use the term change and decay, not decadence. That has a certain negative connotation, and this business about positive and negative aspects of numbers doesn't really fit in with contemporary applied Arithmancy. At any rate, it was a good answer. Now does anyone else have any questions or comments or additions concerning last lesson? If not, then we will move on and I will answer the questions that students submitted in their previous homework. Those of you who have not submitted it, you have until the 12 AM on the 24th."

He then wrote carefully on the board:

Identity numbers - Numbers that through one of the four arithmetic operations return the identity of the number they are paired with.

Zeroeth Theorem of Arithmancy - All magic tends towards decay; save the exceptions covered in higher theorems.

Professor Fox sighed, and nodded. "Okay then, we will move right along I suppose." He pulled out some parchment from his satchel and skimmed through it quickly, then stated, "Now the first question in the homework that was offered was the following: 'How does an arithmancer reduce a magical spell to numbers?'" He leaned against the front desk and turned to the classroom.
"Now, in the kind of Arithmancy we are addressing in this term, we are learning about the inherent magical properties in numbers so as to be able to understand magic and magical spells unfamiliar to us. As such, using those properties, one examines a given magical spell and sees what its properties are, and what happens to the magic under certain circumstances. Then a well trained Arithmancer may figure the number associated with that spell and work backwards to find the set of known magical spells that can be used to break it." He paused for a moment to let the students take it in.

"Each magic spell can be represented by a given prime number, such as 101 for instance. Deciding which number to give to a spell requires quite a bit of practice, intuition, and lots of experience as well as numerous attempts. The number 101 for example is prime, symmetric, purely composed of identity numbers, contains no composites, no 7, 2, 3, or 5. So if it corresponded to a magical spell (which it doesn't) the spell would be very short lived, have little connection to the physical world, and have a rather intuitive method of delivery as it contains no 2 or 3.
"This is again, simply the threshold examining this number. We haven't seen how it changes under operations with other numbers. Suffice it to say, it is a very complex process and requires years of training outside of Hogwarts." He took a breath, then continued, "This is the reason we are learning the properties of numbers first. Only be having a good understanding of the properties of numbers can you be trained to carry on advanced Aritmancy work outside of school. Are there any questions before I move to the next question?"

Nadia had a question, but it was one she was pretty sure she couldn't ask in here. Instead, she waited silently and for Fox to move along. She wrote down the part about Arithmancers deciphering the numbers in magic to find counter-curses. Took notes about properties of numbers such as the 101, too.

She finally raised her hand, even though it was a homework question she thought she would be inventing rather than knowing when handing her homework and that wouldn't do. She asked, "Professor, the decay of a spell or to transform it to zero, how it is possible? Must we understand that a curse is a random number such as 7 and the counter curse -7, a negative number, so that the addition results in zero?

"And if so, how can we make a negative numbered spell?"

Erica noted down what the professor had said without a word. She was strangely quiet at the moment, deciding on just listening and taking in what was being taught. She didn't have any questions relating to the subject matter. Well, not yet, anyway.

Professor Fox looked up at Nadia. "Ah. A good question,but I'm afraid it's not that simple Ms. Rey. Arithmancers simply represent magic with numbers. Thus, it may be that after discovering the properties of some ancient curse that for argument's sake adds two heads to someone. Few will know what the exact spell is, or what it's counter curse is. However, a trained Arithmancer can deduce from that and other things how to represent that spell. Then, let us say it is equal to the sum of two prime numbers that represent modern known spells, potions, runes, etc. The addition of the spells might lead to a way to by-pass the curse, not cure it.
"Hence, it depends on what you know of the original spells, what you know of modern spells, what you know of numbers, and what you know of Arithmancy. As Ms. Arbon said in an earlier lesson, there is no set way to bypass or break a curse. It is a matter of being able to figure out clever methods to do it. There is no set way to break curses. And there is no way to do it based on Arithmancy alone. Indeed, there is no Arithmancy witout your other subejcts. But without knowing Arithmancy and Arithmantic properties of numbers, one would never be able to understand ancient spells in a practical way.
"Lastly, there is no such thing as a negative spell. Numbers only represent properties, and the four basic arithmetic operations represent ways to combine said properties. Any other questions?"

Nadia titled her head, "The addition, not the subtraction?" she blurted mechanically but kept listening. She made a mental note about the non-existance of negative numbers. But that last question might not be completely useless.

"Professor," she raised her hand again, "You say it's possible to use the four basic arithmetic operations. I was thinking the addition of two spells would be mixing them, like, send the two spells at the same time into one hex. If that would be the "addition" of spells, which would be the subtraction? And how about multiplication or divition of spells?"

Professor Fox held up his hands for Nadia to stop. "Yes Ms. Rey, you are as always over-eager. We are getting far afield however. Now, back to the questions. The second question asked was: 'Can the power of zero (the zeroeth law of arithmancy) be used to cause a spell to decay more rapidly?'
"The answer is of course yes, but at once no. But it should come as no surprise to anyone. It is possible to cause things to decay, to grow, to stabalize, to do whatever one wants if one knows the proper spells. This has in all likelihood been taught to you in other classes. One can always reverse a transfiguration or find an antidote to a poison. What the zeroeth law really is indicating is that magic spells left on their own devices have a tendency to lose potency. Just as bread, mice, books, inter-house cooperation, and children's bedrooms all have a tendency to fall into disarray when left untended. However for all spells intended to force something to happen, there is always a spell or spells to get around it. The question is finding the correct combination.
"Again, I emphasize that numbers represent ways to understand spells that may be cast in ancient Egyptian, Sanskrit, Pali, Chinese, or Hopi and as such, the universality of numbers show certain characteristic universalities." He sighed and took a brief moment to enjoy the silence of the classroom befor einevitably asking, "Are there any questions?"

Nadia's eyes who had grown bright with anticipation dulled again. It was extra hard to follow Fox, and having half answers for everything didn't help. Each time she felt she was more lost and even as she thought she was finally understanding, Fox did that, stop the digging. Well, but it was frustrating! It seemed Fox thought the students weren't interested in that and that wasn't the case.

Well, it wasn't her case.

She went back to take notes, a bit frustrated Fox seemed to beg for answers and then didn't respond any of her doubts. At least it was covering the doubts more or less. One to find the counter spell and potions. Zeroeth law, decaying with time. "Can be forced but not immediate," she repeated under her breath as she wrote it down. Then she put her quill down. And there they went again...

Well, what do you think? Nadia crossed her arms and leaned back on her seat, mentally pouting.

After scrawling Peony Tan, 6th year, Ravenclaw messily over her slate, Peony raised her hand. "What do you mean by characteristic universalities?" she asked. Peony was always wary in any class, but more so in Fox's, because she was exceedingly bad with numbers. Also, she was a little frightened of the teacher.

Pfffft.

WHAT?

You're frightened of everything.

I am NOT!

Violet scribbled her name and her year and her house.

Lee stared absoloutley confused by the whole thing. He wished he had attened the last two lessons who he would actually understand what the Professor was on about. He listened carefully anyways and noted down what he felt were important facts.

Violet was also lost on what was going on but listenined to the proffessor anyways.